Question

Determine a soma dos 6 termos da pg crescente em que os extremos são 1/9 e 27

Answer 1

$a_1=\dfrac{1}{9}$

$a_6=27$

$a_1\cdot q^5=27$

$\dfrac{1}{9}\cdot q^5=27$

$q^5=\dfrac{27}{\frac{1}{9}}$

$q^5=243 \iff q=\sqrt[5]{243} \iff q=3$

$S_n=\dfrac{a_1\cdot(q^{n}-1)}{q-1}$

$S_6=\dfrac{\frac{1}{9}\cdot(3^{6}-1)}{3-1}$

$S_6=\dfrac{\frac{1}{9}\cdot728}{2}$

$S_6=\dfrac{728}{18}$

$\boxed{S_6=\dfrac{364}{9}}$